Many Troubleshooing help Articles pointing to checking the Setup, the Config (as mentioned in the above Link), recreate rlauncher (rlauncher.config) and so on. Most of these are good points but often lead not to the solution.

When the TSQL R-Script is executed, nothing really happens, except the Error still is there. So, it seems, that the main cause is permission.

If set the Lauchpad Service to the same Service Account as the SQL Server Service and the SQL Server Agent Service, solved in many Server environments the issue. The SQL Server Service Account is typically correct configured with the necessary User-Rights. So, the Launchpad Service will start and SQL Server can access the Launchpad Runtime to execute the Script correctly!